Topological mirror symmetry for parabolic Higgs bundles

We prove the topological mirror symmetry conjecture of Hausel-Thaddeus (Hausel and Thaddeus, 2001, 2003) for the moduli space of strongly parabolic Higgs bundles of rank two and three, with full flags, for any generic weights. Although the main theorem is proved only for rank at most three, most of the results are proved for any prime rank

An overview of the literature concerning the oceanography of the eastern North Atlantic region

An overview of the main oceanographic features of the eastern North Atlantic boundary, with emphasis toward the upper layers, is presented. The principal features discussed are: water mass boundaries; forcing by wind, density and tides; topographic features and effects; fronts; upwelling and downwelling; poleward flows; coastal currents; eddies. The occurrence and spatial and seasonal variability of these features is described in five regional sections: Celtic Sea and western English Channel; Bay of Biscay; western Iberia; Gulf of Cadiz; northwest Africa. This paper is intended to provide a base of physical oceanographic knowledge in support of research in fisheries, biological and chemical oceanography, and marine biology

On Eulers Rotation Theorem

Summary: It is well known that a rigid motion of the Euclidean plane can be written as the composition of at most three reflections. It is perhaps not so widely known that a rigid motion of n-dimensional Euclidean space can be written as the composition of at most n + 1 reflections. The purpose of the present article is, firstly, to present a natural proof of this result in dimension 3 by explicitly constructing a suitable sequence of reflections, and, secondly, to show how a careful analysis of this construction provides a quick and pleasant geometric path to Eulers rotation theorem, and to the complete classification of rigid motions of space, whether orientation preserving or not. We believe that our presentation will highlight the elementary nature of the results and hope that readers, perhaps especially those more familiar with the usual linear algebra approach, will appreciate the simplicity and geometric flavor of the arguments

Unramified covers and branes on the Hitchin system

We study the locus of the moduli space of GL(n, C)-Higgs bundles on a curve given by those Higgs bundles obtained by pushforward under a connected unramified cover. We equip these loci with a hyperholomorphic bundle so that they can be viewed as BBB-branes, and we introduce corresponding BAA-branes which can be described via Hecke modifications. We then show how these branes are naturally dual via explicit Fourier-Mukai transform (recall that GL(n, C) is Langlands self dual). It is noteworthy that these branes lie over the singular locus of the Hitchin fibration. As a particular case, our construction describes the behavior under mirror symmetry of the fixed loci for the action of tensorization by a line bundle of order n. These loci play a key role in the work of Hausel and Thaddeus on topological mirror symmetry for Higgs moduli spaces. (C) 2020 Published by Elsevier Inc

SO(p,q)-Higgs bundles and Higher Teichmuller components

Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such 'exotic' components in moduli spaces of of SO(p, q)-Higgs bundles on closed Riemann surfaces or, equivalently, moduli spaces of surface group representations into the Lie group SO(p, q). Furthermore, we discuss how these exotic components are related to the notion of positive Anosov representations recently developed by Guichard and Wienhard. We also provide a complete count of the connected components of these moduli spaces (except for SO(2, q), with q >= 4)

Cyclic behaviour of stone and brick masonry under uniaxial compressive loading

An experimental research concerning the uniaxial compressive behaviour of stone and brick specimens, as well as masonry prisms, is presented. Local sandstone and clay brick materials were used in order to obtain results representative with respect to local constructions. Aiming at a comprehensive material description, a set of displacementcontrolled experiments were carried out, both under monotonic and cyclic compressive loading. The procedure adopted for testing is described and the results are discussed, namely material brittleness, intrinsic variability, energy dissipation and stiffness degradation.Dans cet article une recherche expérimentale à propos du comportement en compression uniaxial de spécimens de pierre et de la brique, aussi bien que prismes de maçonnerie, est présenté. Grès et brique de l’argile locale ont été utilisés pour obtenir des résultats représentatifs en ce qui concerne les constructions locales. Avec l’objective de obtenir une description matérielle complète, un ensemble de tests contrôlé par déplacement a été emporté, sous chargement de compression monotonic et cyclique. La procédure adoptée pour tester est décrite et les résultats sont discutés, nommément la fragilité matérielle, variabilité intrinsèque des matériaux, dissipation d’énergie et déchéance de la raideur

Diurnal variability of inner-shelf circulation in the lee of a cape under upwelling conditions.

The nearshore circulation in the lee of a cape under upwelling conditions was studied using in-situ data from 3 consecutive summers (2006–2008). Focus was given to a period between 20 July and 04 August 2006 to study the diurnal variability of the cross-shelf circulation. This period was chosen because it had a steady upwellingfavourable wind condition modulated by a diurnal cycle much similar to sea breeze. The daily variability of the observed cross-shelf circulation consisted of three distinct periods: a morning period with a 3-layer vertical structure with onshore velocities at mid-depth, a mid-day period where the flow is reversed and has a 2-layer structure with onshore velocities at the surface and offshore flow below, and, lastly, in the evening, a 2-layer period with intensified offshore velocities at the surface and onshore flow at the bottom. The observed cross-shelf circulation showed a peculiar vertical shape and diurnal variability different from several other systems described in literature. We hypothesize that the flow reversal of the cross-shelf circulation results as a response to the rapid change of the wind magnitude and direction at mid-day with the presence of the cape north of the mooring site influencing this response. A numerical modelling experiment exclusively forced by winds simulated successfully most of the circulation at the ADCP site, especially the mid-day reversal and the evening's upwelling-type structure. This supports the hypothesis that the cross-shelf circulation at diurnal timescales is mostly wind-driven. By analysing the 3D circulation in the vicinity of Cape Sines we came to the conclusion that the diurnal variability of the wind and the flow interaction with topography are responsible for the circulation variability at the ADCP site, though only a small region in the south of the cape showed a similar diurnal variability. The fact that the wind diurnally undergoes relaxation and intensification strongly affects the circulation, promoting superficial onshore flows in the leeside of Cape Sines. Despite the small-scale nature of the observed cross-shelf circulation, onshore flows as the ones described in this study can be particularly helpful to understand the transport and settlement of larvae in this region and in other regions with similar topography and wind characteristics.We thank D. Jacinto and T. Silva for help during field work and the Port of Sines Authority (APS) for providing oceanographic and meteorological data. Financial support was provided by FCT (POCI/ MAR/57630/2004; PTDC/BIA-BEC/103734/2008 and PEst-OE/ MAR/UIO199/2011). The simulations were preformed in the computational facilities provided under FCT contract RECI/GEO-MET/0380/ 2012. Luísa Lamas was funded by the FCT under a Ph.D. grant (SFRH/ BD/69533/2010)